PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Evaluate:  \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is

The value of \[\int\frac{1}{x + x \log x} dx\] is

\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 8x + 12 on [2, 6] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 4x + 3 on [1, 3] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = (x − 1) (x − 2)² on [1, 2] ?

Verify Rolle's theorem for the following function on the indicated interval  f (x) = x(x − 1)² on [0, 1] ?

Verify Rolle's theorem for the following function on the indicated interval  f (x) = (x² − 1) (x − 2) on [−1, 2] ?

Verify Rolle's theorem for the following function on the indicated interval   f (x) = x(x − 4)² on the interval [0, 4] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = x(x −2)² on the interval [0, 2] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = x² + 5x + 6 on the interval [−3, −2]  ?

Verify Rolle's theorem for each of the following function on the indicated interval f (x) = cos 2 (x − π/4) on [0, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = sin 2x on [0, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = cos 2x on [−π/4, π/4] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = e^x sin x on [0, π] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = e^x cos x on [−π/2, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = cos 2x on [0, π] ?